Journal of Advanced Transportation, Vol. 29, No. 2, pp. 183-192. A Study on Adjustment Factors for U-Turns in Left-Turn Lanes at Signalized intersections Introduction Shou-Min Tsao Song- Wei Chu U-turns are treated as left-turns in the current procedures for estimating saturation flow rates at signalized intersections. While U- turning vehicles are usually mixed with left-turning vehicles in inside or left-turn lanes and conflict with opposing through traffic as left-turning vehicles, the vehicleoperating characteristics are different. Theobjective of this paper is to investigate the effects of U-turns on the traffic flow in left-turn lanes. Field data of 600 headways of left-turning passenger cars and 160 headways of U-turning passenger cars are recorded. The average headways of U-turning passenger cars are found to be significantly larger than those of left-turning passenger cars. The effects of U-turning vehicles depend upon the percent of U-turning vehicles in the left-turn lane, as well as the order of formation in the traffic stream. Adjustment factors for varying percents of U-turning vehicles in left-turn lanes are established. The traffic streams in left-turn lanes are usually composed of left-turning and U-turning vehicles. In the current procedures for estimating saturation flow rates at signalized intersections, U-turns are treated as left-turns. While U-turning vehicles are usually mixed with left-turning vehicles in inside or left-turn lanes and conflict with opposing through traffic as left-turning vehicles, the vehicle operating characteristics are different. The objective of this paper is to investigate the effects of U-turns on the traffic flow in left-turn lanes by measuring average headways in the field. Current Practices In estimating saturation flow rates, adjustment factors are applied to account for the effects of roadway, vehicle composition and turning percentages other than the saturation flow rates under ideal conditions. According to the 1985 Highway Capacity Manual (Transportation Research Board, 1985), the saturation flow rate of an approach of a signalized intersection can be calculated by the Shou-min Tsao, Associate Professor, and Song-Wei Chu a Ph.D. Candidate, are in the Department of Civil Engineering, National Taiwan University, Taipei, Taiwan.
S.M. Tsao and S. W. Chu where S= so = N= fw = fhv = $: P- fbb = fa = ~RT = ~LT = saturation flow rate for the subject lane group under prevailing conditions (vphg); ideal saturation flow rate per lane (pcphgpl); number of lanes in the lane group; adjustment factor for lane width; adjustment factor for heavy vehicles; where a heavy vehicle was defined as any vehicle having more than four tires touching the pavement; adjustment factor for approach grade; adjustment factor for the existence of and the parking activities in a parking lane; adjustment factor for the blocking effect of local buses stopping within the intersection area; adjustment factor for area type; adjustment factor for right turns in the lane group; adjustment factor for left turns in the lane group For exclusive left-turn lanes with a protected signal phase, the adjustment factors for left-turns are taken as 0.95, regardless of the characteristics of the traffic stream. The British practice (Webster and Cobbe, 1966) is to estimate the saturation flow rate of right-turning vehicles, which is equivalent to left-turning vehicles under the right-side driving system, by using the following equation: where S = 1 80 / (1+ 5/r) (2) S = r = saturation flow rate for right-turn lanes (pcu/hr) radius of curvature (ft) The equation shows that the saturation flow rate increases with increasing turning radius. For through vehicles, the saturation flow rate become 1800, because the turning radius approaches infinity. Since the turning radii for U-turns are usually smaller than left-turns, or right-turns in the British system, it is anticipated that U-turns will
A Study on Adjustment Factors for U-Turns.., 185 affect the saturation flow rate to a larger extent. However, this equation was never verified in the relations of left-turns and U-turns. In Australia (Akcelik, 19Sl), the saturation flow rate is calculated by using the following equation: S = estimated saturation flow rate (veh/hr); sb basic saturation flow rate (tcu/hr, tcu=through car unit); f, = lane width factor; f = gradient factor; ( = tcu s per vehicle for a particular vehicle type and turning traffic mix. The factor fc is calculated by where q. 1 = q = e., = fc = (E ei x qi) / q (4) flow in vehicles for vehicle-turn type i; total movement flow (veh/hr); through car equivalent of vehicle-turn type i (tcdveh). The normal conditions in Table 1 refers to a site condition with a minimum turning radius of not less than 15 meters, and with no pedestrian disturbances. A tcu of 1.25 is used for turning radii smaller than 15 meters. As in other countries, the effects of U- turning vehicles are not differentiated. Table 1. Through Car Equivalents (tcuheh) for Different Types of Vehicle and Turn II I I UnopposedTurn I II 11 Vehicle Type I Through I Normal I Restricted I Opposed Turn 11 car I 1 1 1.25 eo II I Heavyvehicle i 2 I 2 I 2.50 I m+l I The effects of U-turns are not differentiated in the highway capacity manuals of Taiwan (Institute of Transportation, 1990), Japan (Japanese Road Federation, 1984), and Canada (Teply and Jones, 1991).
186 S.M. Tsao and S. W. Chu Headway Characteristics According to the 1992 Traffic Engineering Handbook (Pline, 1992), headways are defined as the time interval between the passage of successive vehicles going by a fixed point on the roadway. Any point on the vehicle could be used in timing of headways, as long as the same point is used consistently for all vehicles. In maneuvering a U-turn, a larger space for vehicle maneuver, with a smaller turning radius is usually needed than for left-turns. Therefore, a U-turning vehicle tends to maintain a larger spacing from the rear of its preceding vehicle when compared with a leftturning vehicle. In this study, the rear of vehicles were taken as the reference point for timing of headways. This was considered necessary if the effects of the vehicular characteristics and operating behavior of leading vehicles on the car-following behavior of the succeeding vehicles are to be fully accounted for. Field Measurements In order to compare the traffic flow characteristics of U-turning and left-turning vehicles, two intersections in Taipei were selected. Headways between U-turning and left-turning vehicles were recorded by using a video camera. The selection of intersections for measurement was based on the following criteria: exclusive left-turn lane and protected signal phase for left turns; grade-separated pedestrian facilities to minimize effects of pedestrians; significant number of U-turns; significant proportion of left-turning vehicles; free of disturbances from cross-streets in dissipating leftturning vehicles; no parking allowed; and insignificant disturbances from bus stops. The intersections selected are at Chengte Road and Minchuan West Road (Intersection A), and at Hoping East Road and Hsinsheng South Road (Intersection B) in Taipei. All approach legs have pavement widths of 30 meters or greater, which constitute unconstrained operating conditions for U-turns. The layouts of the two intersections are shown in Figure 1.
A Study on Adjustment Factors for U-Turns... 187 e c t *_- grttr Intersection A Intersection B Figure 1. Layouts of Intersections. According to a study by Hsu on the traffic flow characteristics in Taipei (Hsu, 1982), the headways between vehicles stabilize from the fifth discharged vehicle after the turn of green. Thus, only the headways after the fifth discharged vehicle were recorded. The sampling periods are during morning and evening peak hours, when there are a significant number of U-turning vehicles. A sample of 760 headways, including 600 left-turning vehicles and 160 U-turning vehicles in the left-turn lanes, were recorded. The recorded headways were grouped into four categories, as shown in Figure 2: a. b. c. d. hll: a left-turn preceded by a left-turn; hlu: a left-turn preceded by a U-turn; hul: a U-turn preceded by a left-turn; and huu: a U-turn preceded by a U-turn; Table 2 shows the measured average headways in the four categories. The following observations are made: 1. The headways of a left-turning or a U-turning vehicle are affected by the turning movements of preceding vehicles, especially for U-turns. 2. The left-turns, the average headways are 1.64 and 1.78 seconds for vehicles preceded by a left-turning and a U- turning vehicle, respectively. 3. For U-turns, the average headways are 2.09 and 3.87 seconds for vehicles preceded by a left-turning and a U-
188 S.M. Tsao and S. W. Chu 4. 5. 6. 7. turning vehicle, respectively. With a single U-turning vehicle in a left-turning stream, an additional 0.59 second, or (1.78 + 2.09) - (1.64 x 2), would be required for dissipating the traffic stream in the left-turn lane. If there are two U-turning vehicles in the traffic stream, the additional time required would range from 1.1 8 seconds to 2.82 seconds, or (1.78 + 3.87 + 2.09) - (1.64 x 3), depending upon whether U-turns arrive successively. When preceded by a left-turning vehicle, the average headway of U-turning passenger cars is 1.27 times that of left-turning passenger cars. When preceded by a U- turning vehicle, however, the average headway of U-turns in 2.17 times that of left-turns. The larger the percent of U-turn, the greater the effects of U-turns on the saturation flow rates. The effects of U-turns are expected to increase under more restrained geometric conditions. left-turning left-turning left-turning U-turning U-turning left-turning U-turning U-turning Figure 2. Categories of Headways Adjustment factors for U-Turns Since saturation flow rates in a left-turn lane are dependent upon the percent of U-turns in the lane, as well as the order of traffic stream formation, the average headway of the mixed traffic flow can only be determined after confirming the arrival distribution of U-turning vehicles.
~ A Study on Adjustment Factors for U-Turns... 189 However, the upper limit of the adjustment factors is valid when the average headway is at a minimum, which occurs when there are no successive U-turns. It is derived as follows: hmin (a) = [l - (2a/100)] x hll + (a/100) x hlu + (d100) x hul(5) S,, (a) = 3600 / hfin (a) (6) fm,(a) = Sm,(a)/SL = [3600hmin(a)l/ [ ~~W~LLI = h~lhmin(a)(7) the lower limit of average headway with a % of U- turning vehicles; the average headway between two successive leftturning vehicles (sec); the average headway of a left-turning vehicle, preceded by a U-turning vehicle (sec); the average headway of a U-turning vehicle, preceded by a left-turning vehicle (sec); saturation flow rate of all left-turning vehicles (pcphgpl); the upper limit of saturation flow rate with a % of U- turning vehicles (pcphgpl); the upper limit of adjustment factors for U-turns, with a % of U-turning vehicles; and percent of U-turning vehicles. Category ~ L L ~ L U ~ U L hvv No. of Sample 500 100 100 60 AverageHeadway 1.64 1.78 2.09 3.87 Variance 0.04 0.06 0.06 0.06 By substituting the terms of hll, hlu, hul, by field measured data, and Equation (5) into Equation (7), the upper limit of the adjustment factors for U-turns can be calculated, as shown in Table 3. On the other extreme, the lower limit of the adjustment factors as a function of percent of U-turning vehicles can be derived by the
190 S.M. Tsao and S. W. Chu following equations: h, (a) = [ 1 - (a / 1001 x hll + (a / 100) x h, (8) Smin (a) = 3600 / h, (a) (9) where h, (a) : the upper limit of average headway with a % of U-turning vehicles; h, : the average headway between two successive U-turning vehicles (sec); Smin (a) : the lower limit of saturation flow rate with a % of U- turning vehicles (pcphgpl); and fmin (a) : the lower limit'of adjustment factors for U-turns, with a % of U-turning vehicles. Table 3. Adjustment Factor for U-Turns By substituting the terms of hll, huu by field measured data, and Equation (8) into Equation (1 0), the lower limit of the adjustment factors for U-turns can be calculated, as also shown in Table 3. The average value of the upper and lower limits of the adjustment factors may be adopted for determining the saturation flow rates of a left-turn lane with various percent of U-turning vehicles, as also shown in Table 3. The previous analysis shows that U-turning vehicles cause considerable effects on the traffic flow in a left-turn lane. These effects should be accounted for by adopting the adjustment factor for U-turns in calculating saturation flow rates for left-turn lanes. Conclusions and Recommendations This investigation leads to the following conclusions and recommendations:
A Study on Adjustment Factors for U-Turns... 191 1. The average headway of U-turning vehicles is larger than that of left-turning vehicles. Moreover, U-turning vehicles cause greater effects to their succeeding vehicles than left-turning vehicles. 2. When preceded by a left-turning vehicle, the average headway of U-turning passenger cars is 1.27 times that of left-turning passenger cars. When preceded by a U- turning vehicle, however, the average headway of U- turning passenger cars is 2.17 times that of left-turning passenger cars. 3. The larger the percent of U-turning vehicles, the greater their effects on the traffic flow. The adjustment factor also depends upon the distribution of arrivals of U-turning vehicles. 4. U-turns should be differentiated from left-turns in determining the saturation flow rates of left-turn lanes. 5. The adjustment factor for U-turning vehicles, as derived in this paper, accounts for the motorist behavior in Taipei, Taiwan. Field measurements in other areas are needed to establish adjustment factors suitable for local areas in other parts of the world. 6. The sample sites in this study are characterized by unconstrained operating conditions for U-turns, with curb-tocurb distance of 30 meters. It is expected that the effects of U-turns would be even more significant if the width of pavement is not as great. Similar studies should be undertaken to investigate the effects of U-turns under varying geometric conditions. References Transportation Research Board. 1985. Highway Capacity Manual. Special Report 209. Webster, F.V. & Cobbe, B.M. 1966. Traffic Signals. Ministry of Transport. Road Research Technical No. 56. HMSO London. Akqelik, R. 1981. Traffic Signals: Capacity and Timing Analysis. Australian Road Research Board. Research Report ARR No. 123. Institute of Transportation, Ministry of Transportation & Communications, Republic of China. 1990. Highway Capacity Manual for Highways in Taiwan Area. Japanese Road Federation. 1984. Capacity of Highways. Teply, S. & Jones, A.M. 1991. Saturation Flow: Do We Speak &he
I92 S.M. Tsao and S. W. Chu Same Language? Transportation Research Record, 1320. pp. 144-153. Pline, J.L. Editor. 1992. Traffic Engineering Handbook, 4th Edition. Institute of Transportation Engineers. Hsu, T.P. 1982. Development of Critical Flow Analysis at Signalized Intersection. Master s Thesis. National Taiwan University.